A delivery company runs trucks all the time. A new truck is cheap to run but loses value fast. An old truck costs little to hold but more in repairs every year. Replace too early and capital cost bites. Replace too late and the repairs eat the savings. The question is not whether to buy a truck but how long to keep each one before buying the next.
This topic covers asset replacement decisions, the idea of a replacement cycle, the cash flows that matter (purchase, running costs, resale, tax), why present values of different lives cannot be compared directly, the equivalent annual cost (EAC) method, and the limits of the method. The previous topic covered lease or buy decisions. The next covers capital rationing.
Neither the May 2014 nor the November 2014 Pathfinder sets a stand-alone question on this topic.
In 30 seconds
An asset replacement decision picks the least-cost replacement cycle for an asset needed for ever, replaced by an identical one each time. For each cycle length, work out the PV of cost over one cycle (purchase, running costs, minus resale). You cannot compare these directly because the cycles differ in length. Convert each to an equivalent annual cost: EAC = PV of cost over the cycle ÷ annuity factor for n years.
Choose the cycle with the lowest EAC. Running costs rise with age and resale value falls, so there is usually a trade-off. The method ignores inflation, technology change, changes in the replacement price and capital rationing unless they are built in.
Key terms in plain English
| Term | What it means |
|---|---|
| Replacement cycle | The number of years an asset is kept before it is replaced |
| Least-cost cycle | The cycle with the lowest equivalent annual cost |
| PV of cost | The present value of all costs in one cycle, less resale value |
| Equivalent annual cost (EAC) | The yearly cost that has the same PV as the cycle’s costs |
| Annuity factor | The sum of discount factors for the cycle’s years |
| Resale (scrap) value | What the asset sells for at the end of the cycle |
Syllabus check
This topic is in syllabus area B (advanced investment appraisal, 30% of the marks). It covers:
- identifying the optimum replacement cycle of an asset needed continually;
- the equivalent annual cost method and its relevant cash flows.
CAMA 2020 and replacement decisions
The Companies and Allied Matters Act 2020 (CAMA 2020) is the company law of Nigeria.
| Section | What it says | Link to this topic |
|---|---|---|
| s. 305 | A director must act in good faith in the best interests of the company | Replacement timing should keep long-run cost low for the company |
| s. 308 | A director must use the care, diligence and skill of a reasonably prudent director | Directors should test the cost and resale forecasts behind a policy |
| s. 377(1) and s. 378 | Directors prepare statements that follow IFRS and give a true and fair view | Decisions later affect reported assets, profit and cash |
| s. 385 | The directors’ report covers performance and risk | Major plans and risks are reported to shareholders |
The nature of the decision
This is a decision about how often an asset in regular use should be replaced, not whether to buy it once. When an asset reaches the end of its life, it is replaced by an identical one, and so on for ever. We are evaluating the cycle. The rule: choose the cycle that minimises the PV of cost, which in practice means the lowest EAC.
Relevant cash flows
- the purchase cost of the asset;
- running and maintenance costs, which usually rise as the asset ages;
- tax relief on running costs (they are deductible);
- tax relief on the asset through capital allowances;
- the scrap or resale value at the end of the cycle.
The equivalent annual cost method
You cannot simply compare the PV of costs for a two-year cycle and a three-year cycle: one covers two years and the other three, so the comparison is unfair. The steps:
- For each possible cycle, calculate the PV of cost over one full cycle, with the asset bought in year 0 and sold at the end.
- Divide by the annuity factor for the cost of capital and the length of the cycle: EAC = PV of costs ÷ annuity factor (1 to n).
- Select the cycle with the lowest EAC.
The EAC is the constant yearly amount that, discounted over the cycle, gives the same PV of cost. Because each cycle is turned into a yearly equivalent, the cycles can be compared like for like.
ICAN’s example (NTN). A machine costs ₦17,000 and lasts at most three years. Running costs: ₦1,900, ₦2,400 and ₦3,750 in years 1 to 3. Resale values: ₦8,000, ₦5,500 and ₦4,000 at the end of years 1, 2 and 3. Cost of capital 10%. Ignore tax.
- One year.
PV = −17,000 − 1,727 + 7,272 = −11,455.
EAC = 11,455 ÷ 0.909 = ₦12,602. - Two years.
PV = −16,166.
EAC = 16,166 ÷ 1.736 = ₦9,312. - Three years.
PV = −20,521.
EAC = 20,521 ÷ 2.487 = ₦8,251.
Replace every three years.
ICAN’s practice case (LONG). Purchase ₦30,000; maximum life four years; cost of capital 12%. The model answer’s equivalent annual costs are ₦22,595 (one year), ₦17,507 (two), ₦15,784 (three) and ₦15,356 (four), so the machine should be replaced every four years.
Limits of the method
- It assumes the replacement is identical and costs the same. Prices may change and technology may make a new model better.
- It ignores inflation unless the flows are adjusted.
- It assumes the asset is needed for ever.
- It ignores capital rationing: a short cycle needs capital more often.
- Costs and resale values are estimates.
The rules in more depth
Why running costs and resale value pull in opposite directions
Keeping an asset longer spreads its purchase cost over more years but raises yearly running costs and lowers what it sells for. The best cycle is where the two balance.
Why the EAC is divided by the annuity factor
The PV of cost is a lump sum at time 0. Dividing by the annuity factor turns it into the equal yearly amounts that would have the same PV.
Why a close result needs care
When two cycles have almost the same EAC, small errors in forecasts can reverse the ranking. Say so and consider non-financial factors.
Why tax matters
Running costs, allowances and balancing adjustments all affect tax and should be included in each cycle’s cash flows, discounted at the post-tax rate.
Effect on analysis
Build one table per cycle, work out each PV and EAC, rank them and state the recommended cycle with its limits.
Worked examples
Example 1: finding the cycle. A machine costs ₦20,000. Running costs: ₦3,000, ₦4,500 and ₦6,500 in years 1 to 3. Resale: ₦12,000, ₦8,000 and ₦4,000. Cost of capital 10%. Ignore tax.
- One year.
−20,000 − 2,727 + 10,908 = −11,819.
EAC = 11,819 ÷ 0.909 = ₦13,002. - Two years.
−20,000 − 2,727 − 3,717 + 6,608 = −19,836.
EAC = 19,836 ÷ 1.736 = ₦11,426. - Three years.
−20,000 − 2,727 − 3,717 − 4,882 + 3,004 = −28,322.
EAC = 28,322 ÷ 2.487 = ₦11,388.
Replace every three years, but the two-year cycle is very close.
Example 2: why not compare PVs. In Example 1 the PV of cost is ₦11,819 for one year and ₦28,322 for three years.
- The three-year figure is bigger only because it covers three years of cost.
- Per year, it is cheaper: 11,388 against 13,002.
- Always compare EACs, not PVs.
Example 3: the equivalent annual cost of a project. A ₦70,000 investment over five years at 9% must earn the minimum yearly return that gives the same PV.
- Annuity factor (9%, five years) = 3.890.
- Minimum yearly cash return.
70,000 ÷ 3.890 = ₦17,995. - This is the same equivalent-annuity idea used in replacement.
Example 4: a new factor. In Example 1 the new model of the machine is expected to cut running costs by a quarter from year 2 for a company that replaces every three years.
- Adjust each cycle’s running costs and recalculate the EACs.
- The longer cycles become cheaper, so the least-cost cycle may lengthen.
- The EAC method is only as good as the forecasts that go into it.
How to score full marks
- Set out a separate table for each cycle length.
- Show the discount factors and the annuity factor used.
- Convert each PV to an EAC.
- Rank the EACs and recommend the lowest.
- Include tax if the question gives it.
- Comment on limits and non-financial factors.
Common mistakes in the exam
- Comparing the PVs of cost directly.
- Using the wrong annuity factor for the cycle length.
- Putting the resale value in the wrong year.
- Forgetting that costs are negative and resale positive.
- Ignoring a very close result.
- Giving no limits of the method.
Quick revision
- Least-cost replacement cycle = lowest EAC.
- EAC = PV of cost over one cycle ÷ annuity factor for the cycle length.
- Do not compare PVs over different lives.
- Relevant: purchase, running costs, resale, tax.
- Limits: identical replacement, inflation, technology, rationing.
- CAMA 2020: ss. 305, 308, 377(1), 378, 385.
Practice questions
These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer. Full model answers follow the written questions.
Recall check: multiple choice
Recent ICAN papers are written, although older papers such as May 2014 included multiple-choice questions. These questions are for quick recall. The written questions that follow are closer to the exam.
Question 1. An asset replacement decision chooses:
- Whether to buy once
- How often to replace an asset needed for ever
- The tax rate
- The lease type
Show the answer
B. The replacement cycle.
Question 2. The decision rule is to choose the cycle with the:
- Highest PV of cost
- Lowest equivalent annual cost
- Longest life
- Highest resale value
Show the answer
B. It is the least-cost cycle.
Question 3. EAC equals:
- PV of cost ÷ annuity factor
- PV of cost × annuity factor
- PV of cost ÷ discount factor for year 1
- Resale value ÷ cost
Show the answer
A. For the same life and rate.
Question 4. Why not compare PVs of different cycles directly?
- They cover different numbers of years
- They include tax
- They are always equal
- They exclude resale
Show the answer
A. The comparison is unfair.
Question 5. As an asset ages, running costs usually:
- Fall
- Rise
- Stay the same
- Vanish
Show the answer
B. And resale value falls.
Question 6. Resale value is treated as:
- A cost
- An inflow at the end of the cycle
- Ignored
- Depreciation
Show the answer
B. It reduces the PV of cost.
Question 7. A limit of the EAC method is that it:
- Assumes identical replacements and no change in technology
- Ignores the cost of capital
- Needs no forecasts
- Includes sunk costs
Show the answer
A. Among others.
Question 8. Running costs are, for tax:
- Deductible, so tax relief is included
- Not deductible
- Added to profit
- Ignored
Show the answer
A. They reduce taxable profit.
Question 9. If two cycles have nearly equal EACs, you should:
- Pick at random
- Note the closeness and consider other factors
- Choose the shorter
- Ignore the result
Show the answer
B. Forecasts are uncertain.
Question 10. Which section of CAMA 2020 sets the director’s duty of care and skill?
- Section 308
- Section 400
- Section 405
- Section 409
Show the answer
A. Directors should test the assumptions behind a decision.
Written questions
Question 11 (10 marks). (a) Explain the equivalent annual cost method of choosing a replacement cycle. (6 marks) (b) State four limits of the method. (4 marks)
Question 12 (20 marks). Ede Ltd needs a machine for ever. It costs ₦40m. Running costs: ₦5m, ₦8m and ₦12m in years 1 to 3. Resale values: ₦22m, ₦15m and ₦8m at the end of years 1, 2 and 3. The cost of capital is 10% (discount factors 0.909, 0.826, 0.751; annuity factors 0.909, 1.736, 2.487). Ignore tax. (a) Calculate the PV of cost and EAC for each cycle. (12 marks) (b) Recommend the cycle.
(2 marks) (c) Explain two factors that could change the recommendation. (4 marks) (d) Explain why PVs cannot be compared directly. (2 marks)
Question 13 (10 marks). (a) A machine has a PV of cost over a four-year cycle of ₦46.6m. The cost of capital is 12% (annuity factor for four years 3.037). Calculate the EAC. (3 marks) (b) Another machine has an EAC of ₦15.8m over three years. State which is cheaper per year if the first machine’s EAC is as found in (a). (2 marks) (c) Explain how tax would enter the analysis. (5 marks)
Model answers
Show the model answer to Question 11
(a) The method (6 marks). For each possible cycle length, calculate the PV of cost over one cycle, buying in year 0 and selling at the end. (2) Divide by the annuity factor for the cost of capital and the cycle length to get the equivalent annual cost. (2) Choose the cycle with the lowest EAC. (2)
(b) Limits (4 marks). It assumes identical replacements at the same price; ignores technology change; ignores inflation unless flows are adjusted; ignores capital rationing; relies on forecast costs and resale values. Any four. (1 each)
Show the model answer to Question 12
(a) Cycles (12 marks).
- One year.
−40 − 5 × 0.909 + 22 × 0.909 = −40 − 4.545 + 19.998 = −24.55. - EAC = 24.55 ÷ 0.909 = ₦27.0m. (4)
- Two years.
−40 − 4.545 − 8 × 0.826 + 15 × 0.826 = −40 − 4.545 − 6.608 + 12.39 = −38.76. - EAC = 38.76 ÷ 1.736 = ₦22.3m. (4)
- Three years.
−40 − 4.545 − 6.608 − 12 × 0.751 + 8 × 0.751 = −40 − 4.545 − 6.608 − 9.012 + 6.008 = −54.16. - EAC = 54.16 ÷ 2.487 = ₦21.8m. (4)
(b) Recommendation (2 marks). Replace every three years, which has the lowest EAC. (2)
(c) Factors (4 marks). A new technology or model with lower running costs would favour earlier replacement. (2) Inflation in running costs or in the replacement price, or capital rationing, could change the ranking. (2)
(d) Comparing PVs (2 marks). The cycles cover different numbers of years, so a longer cycle has a larger PV of cost simply because it covers more years. (2)
Show the model answer to Question 13
(a) EAC (3 marks). 46.6 ÷ 3.037 = ₦15.3m. (3)
(b) Comparison (2 marks). The first machine’s EAC of ₦15.3m is lower than ₦15.8m, so it is cheaper per year. (2)
(c) Tax (5 marks). Running costs are deductible, so each year’s cost is reduced by the tax relief. (2) Capital allowances give tax savings on the purchase cost. (1.5) A balancing allowance or charge arises when the asset is sold. (1) All flows are discounted at the post-tax cost of capital. (0.5)
Pathfinder on Replacement cycles and the equivalent annual cost method
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Neither the May 2014 nor the November 2014 Pathfinder sets a stand-alone question on this topic. Replacement cycles appear in appraisal questions. Worked examples 1 to 4 show how to apply the method.
Revise first: Worked examples
Questions ask for the cycle with the lowest equivalent annual cost. See the section on the equivalent annual cost method.
Revise first: The equivalent annual cost method
Source: ICAN Pathfinder, Strategic Financial Management. Diets covered: No stand-alone question in the May 2014 or November 2014 Pathfinder.
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